It is known that there exist faults of the propulsion system of an aircraft, in particular faults for which the thrust of at least one engine no longer complies with the command of the pilot, which may have a direct and significant impact on the safety of the aircraft. To alleviate such faults, provision may be made on the aircraft for devices intended to automatically cut off the faulty engine. However, such a cut-off is not possible in all the phases of flight and for all the states of the aircraft.